The optimization of the vault-predicting formula based on the anterior segment measurements from artemis insight 100

To optimize and evaluate the accuracy of the vault-predicting formula generated from a very high-frequency digital ultrasound robotic scanner (Artemis Insight 100). The relationship between the achieved lens vault (LVa) at one month after intraocular collamer lens (ICL) implantation surgery and the predicted vault (LVp) was analyzed by a retrospective study, and an optimized formula was built up. Then, the accuracy of the optimized vault-predicting formula was evaluated in a prospective study by comparing the LVa and the predicted vault from the optimized formula (LVop). The retrospective study included 77 patients (133 eyes) while the prospective study enrolled 90 patients (170 eyes). The difference between LVp and LVa at one month after surgery was statistically significant (P < 0.05), and the linear regression analysis of LVa against LVp yielded a good fit (R2 = 0.68). The optimized vault-predicting formula was LVop (μm) = 1.21 × LVp (μm) + 124.73. In the validation study, the difference between LVop and LVa was not statistically significant (P = 0.10), and a good agreement between LVop and LVa was shown by Bland–Altman analysis. The optimized vault-predicting formula could predict the actual LV after ICL implantation surgery, help to select an appropriate ICL size and reduce the need for re-operation.

Sizing techniques for the ICL have developed over time with the advent of new diagnostic technology and formulas.Previous methods to determine the vaulting include white-to-white (WTW, manually or with imaging systems) distance or sulcus-to-sulcus (STS) diameter using high-frequency ultrasound B-scan biometry (UBM) 15,16 .An online calculation and ordering system (OCOS) was provided by the manufacturer (STAAR Surgical AG, Nidau, Switzerland), which uses the WTW diameter, and the anterior chamber depth (ACD) for recommending the ICL size.Unfortunately, this methodology leads to about 20% of cases ending up outside the accepted vault range (< 250 μm or > 1000 μm) 14,17 .Because the four footplates of the ICL need to be placed in the ciliary sulcus, the accurate measurement of STS diameter has an important effect on the choice of the ICL size 18 .A formula for calculation of the ICL size using STS measurements has also been proposed 19,20 .However, a meta-analysis by Packer 21 concluded that there is no definitive calculation method for ICL sizing.
The aim of the current study was to optimize the formula for predicting the ICL vault from Reinstein et al. 22 using a very high-frequency (VHF) digital ultrasound robotic scanner.The results might yield a better prediction of ICL vaulting and avoid the need for early ICL exchange.

The characteristics of patients
A total of 77 patients (133 eyes) were enrolled in the vault-predicting formula optimization study, while 90 patients (170 eyes) participated in the validation study of the optimized vault-predicting formula.Patient demographics, ICL characteristics, and biometric parameters of the anterior segment for the two groups are presented in Table 1.Unfortunately, no cases of 13.7 mm were included in this study because the eye size of Asian patients is generally small 23 .

The optimization of the vault-predicting formula
In the optimization study, the mean predicted LV (LVp) was 355.25 ± 101.58 μm, and the mean achieved postoperative LV (LVa) at one month after the surgery was 566.44 ± 147.55 μm, which were statistically significant (P < 0.01).Furthermore, linear regression analysis of LVa at one month against LVp yielded a very good fit with an R 2 = 0.68, a slope of 1.21, and an intercept of 124.73 (P < 0.0001) (Fig. 1).The optimized predicted vault is abbreviated as LVop, yielding the following optimized vault-predicting formula: Table 1.Descriptive statistics of the patients for optimization and validation studies of the vault-predicting formula.SE spherical equivalent, CDVA corrected distance visual acuity, IOP intraocular pressure, ECD endothelial cell density, WTW white-to-white distance, SPD scotopic pupil diameter, ACD anterior chamber depth, ACA anterior chamber angle, ACW anterior chamber width, ATA angle-to-angle diameter, CLR crystal lens rise, STS sulcus-to-sulcus diameter, STSL sulcus-to-sulcus lens rise, CBID ciliary body inner diameter.The benefits from the optimized vault-predicting formula In the optimization study using OCOS, the percentages of eyes achieved low, moderate and high vaulting were 3.8%, 79.7% and 16.5%, respectively, and three eyes underwent an ICL exchanging after surgery due to an excessive lens vault (Fig. 3).In the validation study using the optimized lens vault predicting formula, 93.5% of the eyes achieved a moderate vaulting, and the rates of low vaulting and high vaulting were only 1.2% and 5.3%, respectively.Furthermore, ICL exchange was performed for just one eye (0.6%) for the unsatisfactory vaulting.

Discussion
The Artemis Insight 100 system was introduced into our center before the beginning of the study, and the vault-predicting formula was applied according to the manufacturer's instructions.Unfortunately, a significant difference was found between the predicted vault and the achieved vault after surgery, though we investigated that there was a statistical relationship between them.Thus the current study was conducted to optimize the vault-predicting formula, and to evaluate the accuracy of the optimized formula afterwards.Finally, the optimized vault-predicting formula was established with a good degree of fit (R 2 = 0.68).In the validation stage, the optimized formula was proved to be effective, by which the rate of moderate post-operative vault was improved from 79.7% to 93.5%, and the rate of ICL exchange after surgery resulting from an inappropriate vault was greatly reduced.Given that a meta-analysis by Packer 21 showed that 83.6% of eyes would have moderate vault in cases of the WTW-based ICL sizing, the results of this study are superior to the overall results from the WTW-based ICL sizing.It is worth noting that the current optimized formula is specific for measurement from Artemis Insight 100 and is not interchangeable with other diagnostics.
In the current study, 79.7% of the patients achieved moderate vault after surgery using the traditional OCOS method, which is much lower than the 93.5% achieved using the optimized vault-predicting formula.It is possible that the OCOS formula may be designed to obtain a larger postoperative vault because low post-operative low vault increases the risk of cataract in conventional ICL.
To avoid the appearance of excessively low or high vault after ICL implantation, several formulas have been created so far, but most of them only recommended the optimum ICL size.The NK formula version 1.0 developed by Nakumura et al. 24 selected the ICL size based on the anterior chamber width (ACW) and crystal lens rise (CLR) acquired from anterior segment optical coherence tomography (AS-OCT).The fitting degree of the formula was R 2 = 0.69 and the rate of moderate vault achieved after surgery was 71%.In the updated NK formula version 2.0 25 , the fitting degree was relatively stable, with R 2 = 0.61, but the moderate vaulting rate was significantly improved to 91.2%.Malyugin et al. 26 previously reported an ICL size calculation method using the iris pigment end-to-pigment end diameter, which is a component of the total angle-to-angle diameter (ATA) measurement.Even though the details of this calculation formula have not been published, the mean post-operative vault achieved using that formula was 0.53 ± 0.18 mm (range 0.24-0.84mm), with no excessively low or high values.Dougherty et al. 19 collected STS distance preoperatively and the vault postoperatively from 48 patients (73 eyes) of four ophthalmologists who used the VuMax-II high-frequency UBM system (Sonomed Inc., Lake Success, US).The following equation was derived from the data: ICL size = 6.624 + 0.489 (STS) + 0.264, in which the value of STS distance was the only factor determining the ICL size.The formulas mentioned above could recommend the ICL size, but were not able to predict the post-operative vault.Furthermore, there were only four ICL sizes (12.1 mm, 12.6 mm 13.2 mm, 13.7 mm) provided by the manufacture, though the recommended ICL sizes calculated by the formulas were continuous.For example, when the ICL size suggested by the formula was 12.3 mm, it was difficult to determine whether a 12.1 mm or 12.6 mm ICL ought to be implanted.
Igarashi et al. 27 reported a vault-predicting formula, namely the KS formula, based on the measurements of ATA obtained from AS-OCT: post-operative vault (μm) = 660.9× (ICL size [mm] -ATA [mm]) + 86.6 (adjusted R 2 = 0.41).This formula was evaluated in a recent study 28 , and the predicted vault error (postoperative vaultpredicted vault by the KS formula) was 2.6 ± 184.9 µm. Lee et al. 29 enrolled 236 patients, which were implanted a 12.6 mm ICL.A regression formula to predict the postoperative vault was generated as: postoperative vault  Ideally, the STS distance to which the ICL is fixed should be the most critical element to determine the post-operative lens vault.Therefore, the vault-predicting formulas based on the STS distance were introduced.In a recent study, Zhu et al. 31 evaluated AS-OCT and UBM parameters from 83 patients (83 eyes), and investigate the relationship between them and the postoperative vault.Finally, a vault-predicting formula was generated as: postoperative vault (μm) = -1369.05+ 657.12 × ICL size (mm) − 287.41 × horizontal STS diameter (mm) − 432.50 × lens thickness (mm) − 137.33 × vertical STS diameter (mm).This formula demonstrated a good fitting degree, with R 2 = 0.660 and adjusted R 2 = 0.643, though the sample that was collected to develop the formula was relatively small.The current study is the optimization of a vault-predicting formula reported by Reinstein et al. 22 , which also used the anterior segment parameters measured by the Artemis Insight 100 system, including ciliary body inner diameter (CBID), sulcus-to-sulcus lens rise (STSL), ICL size, ICL power and scotopic pupil diameter (SPD).However, the horizontal STS distance was not included in the Reinstein formula, because according to their model, STS was no longer statistically significant after inclusion of the CBID.This was supported by the finding that the lens footplates rested on or dove directly into the ciliary body in 94% of eyes compared to directly at the sulcus in only 6% 22 .In the present study, the predicted vault generated from the Reinsterin formula showed a poor relation with the achieved postoperative vault before optimization, and the result might be explained by the demographic of the population chosen in the study: the patients enrolled in the study by Reinstein et al.  were Caucasian, while the participants included in the present study were Asian people.We will try to valid this optimized formula in our further studies with different human races to demonstrate its wider applicability.The optimized formula in the current study was constructed from the data of 133 eyes, which was a larger sample than the previous studies, and presented a greater fitting degree (R 2 = 0.68) than ever before.However, we failed to perform a separate analysis for each ICL size, and we will try to accomplish it with more patients in the future.
This study has the following limitations.First, the locations of the four haptics of ICL after surgery, which could influence the lens vault, were not investigated 18 .Second, long-term changes in central vaulting because of accommodation or chronologic changes in crystalline lens thickness must also be considered 8 .Third, the accurate measurements of the anterior segment parameters obtained from Artemis Insight 100 relied on the experience of the technician.However, the examiners and surgeons in this study were set, and whether different operators or surgical habits affect the results requires further research.Finally, it costs a lot to buy Artemis Insight 100, so the device is available in few of the refractive centers all over the world.
In conclusion, a vault-predicting formula generated from the anterior segment parameters acquired by the Artemis Insight 100 VHF digital ultrasound robotic scanner was hereby optimized, and the accuracy of this optimized vault-predicting formula was also demonstrated.The optimized vault-predicting formula allows for precise vault prediction, thus enabling appropriate selection of the ICL size.

Design and participants
This study comprised two parts.The first part was a retrospective study to optimize the formula based on the optical parameters obtained from Artemis Insight 100 VHF digital ultrasound robotic scanner (ArcScan, Inc), by comparing the predicted to the achieved vault.The second part involved a prospective study to validate the optimized formula, in which the consistency between the post-operative vault and the vault generated from the optimized formula was analyzed.All patients who underwent ICL surgery at the Refractive Surgery Center of Henan Provincial Eye Hospital between October 2021 and May 2022 were enrolled in the vault-predicting formula optimization study.Subsequently, all patients who received ICL surgery between June 2022 and March 2023 at the same center were enrolled in the optimized vault-predicting formula validation study.All consecutive patients were included in the current study.The study protocol was approved by the Ethics Committee of Henan Provincial Eye Hospital (approval code: HNEECKY-2021-13-02).This study was conducted according to the tenets of the Declaration of Helsinki and informed consent was obtained from all participants.
The inclusion criteria were (1) 21-45 years of age, (2) ACD ≥ 2.8 mm, (3) corneal endothelial cell density (ECD) ≥ 2000/mm2, (4) clear crystal lens, and (5) the rotating angle of the ICL placement no more than 15°.The exclusion criteria were (1) other eye diseases except refractive errors, such as cataracts and glaucoma, (2) systemic diseases such as diabetes mellitus, autoimmune diseases, such as systemic lupus erythematosus and rheumatoid arthritis, or collagen diseases that may affect post-operative healing, and (3) the rotating angle of the ICL placement more than 15°.

Preoperative measurements
Prior to surgery, all patients received a complete ophthalmologic examination, including uncorrected distance visual acuity (UDVA), manifest refraction spherical equivalent (MRSE), corrected distance visual acuity (CDVA).Anterior segment anatomy was assessed with slit-lamp microscope, IOP using a non-contact tonometer (Canon, Irvine, US), and the fundus was observed by indirect ophthalmoscopy.Moreover, the internal ACD from the corneal endothelium, the simulated keratometry, and the WTW were recorded before surgery using Pentacam HR three-dimensional panoramic analyzer (Oculus, Wetzlar, Germany).An IOL Master 700 biometer (Carl Zeiss GmbH, Oberkochen, Germany) was used to measure the axial length.SPD was measured using Scansys www.nature.com/scientificreports/three-dimensional anterior segment analytic system (Mediworks, Shanghai, China).Finally, an EM-3000 corneal endothelial cell counter (Tomey Corporation, Nagoya, Japan) was used to measure corneal ECD.

Artemis insight 100 VHF digital ultrasound scanning
All participants received posterior chamber imaging and biometry using the Artemis Insight 100 VHF digital ultrasound robotic scanner by an experienced technician (DW) according to a previously described protocol 32 .Artemis scans were acquired with the patients in a sitting position with the eye coupled to the ultrasound transducer with a normal saline immersion medium contained in a disposable eye seal.During scanning, the patient gazed at a fixation light and eye position was monitored by an infrared camera.An ICL pre-operational scan set included sweeps at 0, 3, 6, 9, 351, 354, and 357 degrees, for a total of seven horizontal meridians.A minimum of two scan sets were required for each patient, providing at least 14 images to evaluate the horizontal biometry of the posterior chamber, of which the four best images were analyzed by a single observer (WH).The following parameters were measured using software calipers within the Insight 100 system to measure the following parameters: ACD, ACW defined as the sclera spur-to-spur diameter, anterior chamber angle (ACA), ATA, STS, CLR, STSL, CBID defined as the horizontal measurement from ciliary body to ciliary body (Fig. 4).

Surgical procedure
All procedures were carried out under topical anesthesia by the same experienced surgeon (PC).Pupil dilation was initiated with compound tropicamide eye drops (Santen Pharmaceutical Co., Ltd., Osaka, Japan) instilled twice, 10 min apart.To prevent potential cyclotorsion in the supine position during Toric ICL implantation, the 0°-180° horizontal axis was preoperatively marked under the slit-lamp.Oxybuprocaine hydrochloride eye drops (Santen Pharmaceutical Co., Ltd., Osaka, Japan) were used to perform surface anesthesia.Implantation was performed through a 3.0 mm temporal incision, and the anterior chamber was filled with 15 mg/mL medical sodium hyaluronate gel (Qisheng Biological Preparation Co., Ltd., Shanghai, China).The V4c EVO ICL (STAAR Surgical AG) which comes with a central hole, was then inserted via the corneal incision using an injector cartridge (STAAR Surgical AG).After initially placing the ICL on the iris, the four haptics were tucked to the ciliary sulcus under the iris with a bespoke manipulator, and the ICL was rotated to the desired meridian 15.0° or less and its position was fixed horizontally in all cases.On positioning the ICL, the medical sodium hyaluronate gel was washed out of the anterior chamber using a balanced salt solution.Antibiotic (levofloxacin, 0.5%) and corticosteroid (loteprednol etabonate 5 mg/mL) drugs were administered topically four times daily for one week postoperatively, with gradual reduction of the dose thereafter.

Figure 2 .
Figure 2. Bland-Altman plots comparing the values of achieved lens vault at one month after surgery and optimized predicted vault (The solid line in the middle represents the mean difference, and the two dotted lines above and below represent the 95% limits of agreement).

Figure 3 .
Figure 3. Distribution of achieved postoperative lens vault and the percentage of eyes that underwent ICL exchange due to inappropriate lens vault between the optimization and the validation study groups.

Figure 4 .
Figure 4.The parameters measured by Artemis Insight 100 very high-frequency digital ultrasound B scan.(a) Anterior chamber depth (ACD), anterior chamber angle (ACA), anterior chamber width (ACW), angle-to-angle (ATA) diameter, sulcus-to-sulcus (STS) diameter, ciliary body inner diameter (CBID); (b) the lens rise from the ATA plane described as crystal lens rise (CLR, shown as green) and the lens rise from the STS plane named STS lens rise (STSL, show as blue).